Mathematical investigation: Practical uses of right triangles for indirect measurement

Abstract

The purpose of this study was to determine the potential usability of 45°-45°-90° special right triangles to solve the problem of estimating an unknown height and distance. A qualitative-descriptive method was employed, through documentation research, by examine reliable academic texts, and instructional books/references issued not later than 2021. This research would explain how the 45°-45°-90° triangle, with a fixed ratio between its sides of 1:1:2, may make it easy for measuring distances to inaccessible heights and objects like trees, buildings, utility poles and etc. The analysis indicates that the indirect method can successfully resolve the stated issue since with accurate adjustment of 45° of the angle of elevation, the perpendicular distance between the object and observer and the height of the object would be equal and can be calculated quickly. Precise but minor errors limit its real‑world use.